Image texture won't appear correctly in Unity... Fine In Blender (And Yes It's Baked)
Okay, I had to outsource this to a smart person because I'm a beginner and frankly ignorant of all this stuff... but I'm going to post the answer for future newbies like me!

Okay, so the problem was in Blender. Inside the Object Data > UV Maps panel, I had several UV maps left over from my frantic attempts at baking. I had to delete those and re-import the armature+mesh.



Then, in Unity, I followed these steps (I did not need to re-bake my texture by the way):



In Unity, make sure to re-do everything like mark the rig as humanoid and force T-pose and stuff. I was frustrated for an hour because I forgot to do this and couldn't figure out why my animations wouldn't run.